The present invention relates generally to stationkeeping systems and methods for controlling orbiting satellites, and more particularly, to a low earth orbit (LEO) satellite constellation stationkeeping system and method having absolute altitude control.
The following discussion compares two low earth orbit constellation stationkeeping strategies, the first where conventional relative altitude control is performed and, the second where absolute altitude control in accordance with the principles of the present invention is performed. The strategies are discussed with reference to only the low earth orbit regime because a measurable atmospheric drag perturbation is assumed to exist. The goal is to determine the simplest operationally useful constellation stationkeeping algorithm for implementation considering operational constraints such as maneuver windows and limits on maneuver burn durations or delta V""s.
This discussion involves only in-plane stationkeeping maneuvers that control the altitude and argument of latitude of a given satellite within a constellation. Near circular orbits are assumed. Eccentricity control is assumed to be handled independently. That is not to say that eccentricity control is not performed simultaneously with these maneuvers, but rather, that placement of the maneuver with respect to argument of perigee for the purposes of eccentricity control will not be discussed here. Similarly, out-of-plane perturbations are assumed to be handled independently. These are valid assumptions in the Globalstar constellation developed by the assignee of the present invention.
Absolute control versus relative control. A first reference entitled xe2x80x9cStation Keeping Strategies for Constellations of Satellitesxe2x80x9d, by Alain Lamy and Stephane Pascal, Advances in the Astronautical Sciences, Vol. 84, American Astronautical Society, January 1993, states that:
xe2x80x9cThe first method for station keeping of constellations is to control each satellite independently of the others. Each satellite is kept in a box centered on nominal position, affected only by mean perturbations. As phasing with other satellites must be controlled, the mean movement must be the same for all the satellites in the constellation . . . the constellation keeps its properties over time.
The purpose of relative station keeping strategy is to control each satellite with respect to a xe2x80x9cmean constellationxe2x80x9d built upon actual positions of satellites at each time. This mean constellation has to:
have the same properties as nominal constellation (walker properties),
be the closest to all satellites to minimize maneuver cost.
The idea of relative station keeping is to take advantage of global effects of perturbations that do not change the visibility criterion . . . xe2x80x9d
Absolute control is required when strict requirements for phasing of orbits with the Earth""s rotation exist, as is the case on many science missions, Relative control is preferred when such requirements are not imposed, rather only that the relationship between satellites is important. Such is the case for a low earth orbit communications satellite network where percent coverage is the primary criterion.
If a constraint on altitude is imposed on a low earth orbit constellation (due to licensing requirements, for example) while constraints on phasing with the Earth do not exist, then a unique situation arises. In this case, absolute control is required on constellation altitude while satellite positioning (argument of latitude) within the constellation can be maintained using relative control. Given some real operational constraints, such as limited finite sets of maneuver delta V and periodic maneuver windows, it can be shown that a strategy of absolute altitude control can provide the advantage of fewer maneuvers than a relative altitude control strategy over the life of the satellite. This advantage can be achieved with no greater complexity in algorithm implementation and may be computationally less intensive.
Relative altitude control. A second reference entitled xe2x80x9cAutomatic Maneuver Planning for Maintenance of Satellite Constellation Geometryxe2x80x9d, by Peter Brodsky, Lockheed Martin Space Mission Systems and Services, describes a method of constellation stationkeeping where relative control is used for in-plane and out-of-plane stationkeeping. Eccentricity and argument of perigee are not controlled in this scheme. These elements require separate maneuver strategies to account for deviations. This strategy described assumes the following.
(1) Target satellite slots (altitude and argument of latitude) are derived from mean positions of the actual satellites and deviations are derived from the difference of the actual position and the target slot. This is referred to as the deviation from mean deviation.
(2) The altitude is not held constant. Degradation of the constellation altitude due to atmospheric drag is allowed to occur over the life of the system. The algorithm does not attempt to correct for this.
(3) The algorithm follows a feedback control law. Time constants are set according to the desired stationkeeping cycle length.
(4) There is a basic assumption in the feedback control system algorithm that drag operates nearly equally on all the satellites in the constellation.
(5) There is no consideration for eccentricity control. Eccentricity control must be handled separately in maneuver planning.
(6) There is no consideration of minimum/maximum or a limited set of discreet pulse lengths for stationkeeping maneuvers. The control law allows any size delta V in its solution, no matter how small, regardless of physical system constraints or implementation complexity.
(7) Every epoch in time has a maneuver solution for every satellite in the constellation. This means that even immediately following a performed maneuver, a solution for a new maneuver can be produced for the same satellite. Additionally, any single maneuver performed upsets the solution for all other satellites in the constellation, thus requiring recalculation of all other maneuvers. A system designer must guard against an algorithm that produces more maneuvers than are required.
Theoretically, such a closed-loop feedback control system for stationkeeping could reduce the error rate term to nearly zero. This at first would appear to require only a small number of maneuvers over the life of the satellite. However, without some limits on maneuver times, what really results is not fewer maneuvers, but an infinite number of maneuvers growing ever smaller in magnitude. To limit this, maneuvers are only performed when it is necessary to remain in a stationkeeping xe2x80x9cboxxe2x80x9d.
While both stationkeeping strategies are technically similar in implementation complexity, absolute altitude control offers some advantages over relative altitude control. The present invention addresses this control strategy.
Accordingly, it would be advantageous to have a low earth orbit satellite constellation stationkeeping system or method having absolute altitude control.
The present invention provides for an easily implementable satellite constellation stationkeeping algorithm that may be implemented as a system, procedure, or method for maintaining the relative positioning among satellites of a low earth orbit satellite constellation with minimal maneuvering, while maintaining the constellation altitude over the effects of atmospheric drag. Exemplary absolute altitude control satellite constellation stationkeeping algorithms are implemented as follows.
A plurality of satellites are each configured with a controller, or a controller is provided on the ground at a ground station, that implement an absolute altitude control algorithm. The plurality of satellites are launched into a respective plurality of slots of a low earth orbit. The orbital position of each satellite is controlled using the controller and absolute altitude control algorithm such that the respective satellite is allowed to drift to or near the edge of a positional box that defines its slot, and the altitude of the satellite is selectively driven to a fixed target altitude, such as by using one or more thrusters, for example, to reverse the satellite drift in its slot. During normal operation, the orbital position of each satellite is controlled using only posigrade thrusting using the thrusters.
The satellite constellation stationkeeping algorithm makes use of atmospheric drag perturbations to extend the stationkeeping cycle of a satellite in the low earth orbit constellation while simplifying the implementation algorithm and performing minimal maneuvers. The present invention provides for a simple operationally-useful algorithm that implements low earth orbit constellation stationkeeping, considering operational constraints such as maneuver windows and limited maneuver bum durations.
The stationkeeping algorithms provide for reduced requirements for stationkeeping maneuvers. The stationkeeping algorithms provide for maintenance of the constellation altitude at no cost in maneuver cycle.